How can cold radiation heat?

I have enough experience with steam radiators and heat lamps to know that they don't radiate enough heat to warm their surroundings to the temperature of the radiator or lamp. How then can ground and water emit radiation with sufficient energy to warm the air to a higher temperature than the ground or water? The energy in radiation by ground and especially by water, which is a very poor radiator, is far less than the energy radiated by a steam radiator.

Some advocates of greenhouse gases even claim that ground and water can heat the air with radiation to a higher temperature than the ground and water and then have the air heat the ground or water. Such a process would be even better than the goal of con artist inventors -- the perpetual motion machine.

When ground and water are heated by the sun, they begin heating air in thermal contact to their temperature. As the air is heated it moves upward allowing colder air to be heated by conduction. I have serious doubts that radiation energy transfer can heat the air to an even higher temperature considering that the ground a very small fraction of its heat energy is actually converted into radiation per second and the energy received by individual molecules declines by the square of the distance from the ground.

I'm going to take a shot at addressing this issue, but it isn't something that I've studied. To start with, though, a heat lamp or radiator will heat the air surrounding it to its own temperature if that air is confined to the immediate area and doesn't have the opportunity to re-radiate the heat. That is, after all, the basic principle behind clothing, blankets, and wetsuits.
Another factor that you didn't specify is what depth of dirt/water you have in mind. The surface layer of ground during daylight is usually hotter than the air. Dig down a bit and it becomes progressively cooler until it stabilizes at somewhere around 65ºF for quite a fair distance. (That's why underground homes require so little in the way of heating/cooling equipment.) If you've ever tried to walk barefoot on a beach or sidewalk on a hot day, you'll recall that the surface can be intolerably hot.
Finally, the atmosphere absorbs significant heat directly from the sunlight filtering through it rather than just from ground/sea radiation.
That's about the best that I can do for now.

If you heat the air with a certain amount of energy, it raises the temperature. If you heat water with the same amount of energy, the temperature increase is much smaller (for the same amounts of air and water). Water stores a lot of energy, just to move up one degree of temperature.

I have enough experience with steam radiators and heat lamps to know that they don't radiate enough heat to warm their surroundings to the temperature of the radiator or lamp.

This depends not just on the radiator but also on how quickly heat is lost. If you are heating a room in winter, then you are competing against heat being conducted out of the house by the walls. If you are heating a room that is ideally insulated from the outside, then it can reach the same temperature as the radiator. So what you say is not true as a general statement.

reasonmclucus said:

How then can ground and water emit radiation with sufficient energy to warm the air to a higher temperature than the ground or water? The energy in radiation by ground and especially by water, which is a very poor radiator, is far less than the energy radiated by a steam radiator.

Have you ever used a mirror to give something twice the sunlight? Or for example, sat in an enclosure with white walls but no ceiling? You will find it extremely hot, even though the walls (or mirror) remain cool. Similarly, ground and water can reflect radiation, so a lake is much cooler than the surrounding air.

I have enough experience with steam radiators and heat lamps to know that they don't radiate enough heat to warm their surroundings to the temperature of the radiator or lamp. How then can ground and water emit radiation with sufficient energy to warm the air to a higher temperature than the ground or water? The energy in radiation by ground and especially by water, which is a very poor radiator, is far less than the energy radiated by a steam radiator.

Some advocates of greenhouse gases even claim that ground and water can heat the air with radiation to a higher temperature than the ground and water and then have the air heat the ground or water. Such a process would be even better than the goal of con artist inventors -- the perpetual motion machine.

When ground and water are heated by the sun, they begin heating air in thermal contact to their temperature. As the air is heated it moves upward allowing colder air to be heated by conduction. I have serious doubts that radiation energy transfer can heat the air to an even higher temperature considering that the ground a very small fraction of its heat energy is actually converted into radiation per second and the energy received by individual molecules declines by the square of the distance from the ground.

If what you were describing were the case: that the ground could radiate enough heat to raise the temperature of the atmosphere above its own temperature, then this would indeed be a violation of the Second Law of Thermodynamics (most directly the Clausius statement) and allow for a perpetual motion machine in violation of common sense.

However, this is not what people who argue that greenhouse gasses raise the temperature of the earth claim. The argument goes like this: radiation is emmited from the sun with a range of frequencies determined by its temperature. The radiation then reaches the atmosphere, which most of the radiation at these frequencies can pass through. It then reaches the ground where it is absorbed. The ground then re-radiates that energy with a range of frequencies determined by its temperature. Since the earth is cooler than the sum, the radiation emmited by the ground contains a higher fraction of radiation at lower frequencies. The greenhouse gasses are more reflective to these frequencies, and much of it is reflected back. This then heats the ground further. The net effect is that the earth behaves as if it were darker and absorbs a higher fraction of the sun's light. At no point does the ground heat the air to a higher temperature than itself. Greenhouse gasses just reduce the effectiveness of one mechanism for the earth to cool itself. Since it recieves a constant stream of heat from the sun, one would expect the temperature to rise.

The basic greenhouse gas thesis was proposed by French mathematician Jean Baptiste Fourier in the 1820's. He suggested that "light heat" from the sun penetrated the atmosphere and heated what we commonly refer to as the earth's surface.(From a thermodynamic standpoint the earth's surface is the fussy boundary between the atmosphere and the vacuum of space.)

The ground and water were then supposed to radiate "dark heat" that would heat the atmosphere. Fourier and other physicists of the time believed that atoms were the smallest particles of matter and atoms/molecules of air simply absorbed this "dark heat" and became hotter. It would be 70 years before J.J. Thomson discovered that atoms were actually comprised of smaller charged particles. Twenty years after this Neils Bohr discovered that the absorption of specific wavelengths of light by a atom/molecule affected the internal energy state of the electrons in an atom and the atom had to radiate energy of that same wavelength before absorbing any other radiation.

Another major problem with the theory is that the earth's "surface" is primarily covered by water which in solid form reflects light back into space while absorbing only a small portion of it and in liquid form is a poor radiator and even reflects some sunlight back into space. Much of the ground is covered with plants which convert a significant portion of solar radiation into the chemical bonds holding organic molecules together rather than becoming hotter.

This depends not just on the radiator but also on how quickly heat is lost. If you are heating a room in winter, then you are competing against heat being conducted out of the house by the walls. If you are heating a room that is ideally insulated from the outside, then it can reach the same temperature as the radiator. So what you say is not true as a general statement.

Have you ever used a mirror to give something twice the sunlight? Or for example, sat in an enclosure with white walls but no ceiling? You will find it extremely hot, even though the walls (or mirror) remain cool. Similarly, ground and water can reflect radiation, so a lake is much cooler than the surrounding air.

Heated air moves up unless held close to the ground by clouds or high pressure so it doesn't stay in one place very long. Mirror type reflection requires a smooth, preferably solid, surface. Gases only form such a reflective surface under special conditions, such as ionization or forming areas with different refractive characteristics such as air of different temperatures which causes what appears to be light reflectiing from hot highways in rural areas on a hot day.